The Supremum of Chi-Square Processes

Charles-Elie Rabier () and Alan Genz
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Charles-Elie Rabier: Université de Toulouse
Alan Genz: Washington State University

Methodology and Computing in Applied Probability, 2014, vol. 16, issue 3, 715-729

Abstract: Abstract We describe a lower bound for the critical value of the supremum of a Chi-Square process. This bound can be approximated using an RQMC simulation. We compare numerically this bound with the upper bound given by Davies, only suitable for a regular Chi-Square process. In a second part, we focus on a non regular Chi-Square process: the Ornstein–Uhlenbeck Chi-Square process. Recently, Rabier et al. (2009) have shown that this process has an application in genetics: it is the limiting process of the likelihood ratio test process related to the test of a gene on an interval representing a chromosome. Using results from Delong (Commun Stat Theory Method A10(20):2197–2213, 1981), we propose a theoretical formula for the supremum of such a process and we compare it in particular with our simulated lower bound.

Keywords: Chi-Square process; Monte Carlo; Quasi-Monte Carlo; Ornstein–Uhlenbeck process; Quantitative Trait Locus detection; 60G99; 6008; 65C05; 65C10; 65D30; 62M86; 62P10 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-013-9331-1

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